Question

Some colleges now allow students to pay their tuition using a credit card. A report includes data from a survey of 100 public 4-year colleges, 100 private 4-year colleges, and 100 community colleges. The accompanying table gives information on credit card acceptance for each of these samples of colleges.

	Accepts Credit Cards for Tuition Payment	Does Not Accept Credit Cards for Tuition Payment
Public 4-Year Colleges	90	10
Private 4-Year Colleges	65	35
Community Colleges	100	0

For purposes of this exercise, suppose that these three samples are representative of the populations of public 4-year colleges, private 4-year colleges, and community colleges in the United States. Is there convincing evidence that the proportions in each of the two credit card categories are not the same for all three types of colleges? Test the relevant hypotheses using a 0.05 significance level. (Hint: See Example 12.5.)

State the appropriate null and alternative hypotheses.

H₀: The proportions falling into each of the two credit card categories are the same for all three types of colleges. H_a: The proportions falling into each of the two credit card categories are not the same for all three types of colleges.

H₀: The proportions falling into each of the two credit card categories are not the same for all three types of colleges.
H_a: The proportions falling into each of the two credit card categories are the same for all three types of colleges.    

H₀: The proportions falling into each of the two credit card categories are different for all three types of colleges. H_a: The proportions falling into each of the two credit card categories are not different for all three types of colleges.

H₀: The proportions falling into each of the two credit card categories are not different for all three types of colleges. H_a: The proportions falling into each of the two credit card categories are different for all three types of colleges.

Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

χ²=

P-value=

State the conclusion in the problem context.

Reject H₀. There is not convincing evidence that the proportions in each of the two credit card categories are not the same for all three types of colleges.

Fail to reject H₀. There is convincing evidence that the proportions in each of the two credit card categories are not the same for all three types of colleges.    

Reject H₀. There is convincing evidence that the proportions in each of the two credit card categories are not the same for all three types of colleges.

Fail to reject H₀. There is not convincing evidence that the proportions in each of the two credit card categories are not the same for all three types of colleges.

Answer 1

H: The proportions falling into each of the two credit card categories are the same for all three types of colleges. H: The proportions falling into each of the two credit card categories are not the same for all three types of colleges. EXCEL (Mega Stat) output: Chi-square Contingency Table Test for Independence Acce Accepts Credit Cards for Tuition Payment 90 Public 4-Year Colleges Private 4-Year Colleges Community Colleges Total Does Not Accept Credit Cards for Tuition Payment 10 35 0 45 Total 1 00 100 100 300 100 Communicar Cowes 255 50.98 chi-square 2 df 8.51E-12 p-value

r = 50.98 P-value = 0 Reject H. There is convincing evidence that the proportions in each of the two credit card categories are not the same for all three types of colleges.